It is known that the optimal measurement for discriminating binary GS-CS can be described by a projective measurement composed of two orthogonal Schrödinger cat state [1]}. Here, the optimal measurement is described by a projective measurement composed of two orthogonal Schrödinger cat states
\(|\mathcal {C}_\pm \rangle :=\mathcal {N}_{\alpha _0,\alpha _1}^{(\pm )}(|\alpha _0\rangle \pm |\alpha _1\rangle ),\) 
